Line strengthsS for the dipole allowed transitions within then=2 complex of the oxygen isoelectronic sequence have been fitted in the formZ²S=A+B/(Z −C), whereZ is the nuclear charge of a particular ion. The constantsA, B andC are determined by using a non-linear least square method. The data forS are taken from the configuration interaction calculations which included internal, semi-internal and all external type correlations for ions in the rangeZ=8 − 25. It is shown that the values ofA obtained from the fit for all the transitions are in excellent accord with the ab-initio values obtained in the hydrogenic limitZ → ∞ provided near degeneracy effects are included in the ground state multiplet 1s²2s²2p⁴¹S.

The first relativistic correction of orderα² to the dipole polarizability of a hydrogenic ion has been investigated by using mean excitation energy of the ion within the second-order perturbation theory. The density-dependent mean excitation energy is estimated via Bethe theory for the stopping cross section for a moving point charge interacting with the hydrogenic ion. In this approach only the unperturbed Dirac wavefunctions are required to evaluate the appropriate matrix elements. The first relativistic correction turns out to be − (13/12)(αZ)². This has the correct sign and is within 5% of the exact result which is −(28/27)(αZ)².

Line strengthS and radial matrix elementσ for the dipole allowed transitions withinn=2 complex of ions in the Be isoelectronic sequence have been fitted in the formsZ²S=A+B/(Z − C) andZσ=A′ + B′/(Z − C′). The constantsA, B, C andA′, B′, C′ have been calculated by employing a non-linear least square method. The relevant data forS andσ have been taken from calculations which includes correlation effects. It is shown that the fitted yalues ofA andA′ are in excellent accord with their hydrogenic values (Z →α) provided that we express the zeroth-order wavefunction of the ground state 1s²2s²¹S as a quantum-mechanical admixture of the Hartree-Fock (HF) state 1s²2s²¹S and the near-degenerate state 1s²2p²¹S.

The total cross sections for positron impact on hydrocarbons have been calculated using the additivity rule in which the total cross section for a molecule is the sum of the total cross section for the constituent atoms. The energy range considered is from a few eV to several thousand eV. The total cross sections for positron impact on an atom are calculated by employing a complex spherical potential which comprises of a static, polarization and an absorption potential. We have good agreement with the experimental results for hydrocarbons for positron energy ⩾100 eV. Our results also agree with the available calculations for CH₄ and C₂H₂ which employed full molecular wavefunctions beyond 100 eV. Our absorption cross sections also agree with molecular wave-function calculations for C₂H₂ and CH₄ beyond 100 eV. We have shown the Bethe plots fore⁺−C ande⁺−H scattering systems and Bethe parameters have been extracted. We have fitted the cross section for positron impact on hydrocarbons in the formσ_t(C_nH_m)=naE⁻b+mcE⁻d in the energy range 300–5000 eV wherea=195.0543,b=0.7986,c=371.1757 andd=1.1379 withE in eV andσ_t in 10⁻¹⁶ cm².

The total (elastic + inelastic) cross sections fore⁺ impact on alkaline-earth elements from Be to Ra are calculated by employing a complex spherical optical potential. This potential has static, polarization and absorption components. The positron energy range is from a few eV to several thousand eV. We have compared our elastic cross sections for Mg and Ca with the other available results and the agreement is good for energies above 100eV. We have also compared our absorption cross sections withe⁻ ionization cross sections at high energies where our absorption cross sections are in good accord. We have made Bethe plots fore⁺ scattering on these elements.

Transition amplitudes and transition probabilities for the two-photon 1s–2s transition in the hydrogen atom and 1¹s–2¹s transition in helium atom have been calculated using a partial-closure approach. The dominant term is calculated exactly and the remaining sum over intermediate states is calculated using a mean excitation energy. Our value of the transition amplitudes agree within 2% with the exact results for the hydrogen case. Our value of the transition probability for hydrogen is 8.50 s⁻¹ which is in good accord with its known value 8.226 s⁻¹. For helium, the photon energy distribution of the metastable 2¹s state is in good agreement with the accurate values. The corresponding transition probability is 53.7 s⁻¹ which is in good agreement with the accurate value 51.3 s⁻¹.

The open shell molecules with even number of electrons have $\pi^2$ or $\pi^{2}_{g}$ ground-state electronic configuration. Several homonuclear diatomic molecules like $\rm{O_2, S_2, B_2}$ have $\pi^{2}_{g}$ ground state in the $D_{\infty h}$ point group and heteronuclear diatomic radicals like PH, NH, SO have $\pi^2$ ground state in the $C_{\infty v}$ point group. We have computed and presented here the rate coefficient of these open shell molecules $\rm{(O_2, S_2, B_2)}$ and radicals (PH, NH,SO) from the results of our previous studies using a well-established $\it {ab-initio}$ formalism: the $R$-matrix method. The rate coefficients for elastic and electron-excited processes are studied over a wide electron temperature range.

This systematic study reports various electron impact cross-sections, rate constants and transport properties of $NH_2$ radical in the low-energy limit. The collision study is based on $R$-matrix formalism and involves the use of various scattering models employing different active spaces. Both electron excited inelasticcross-sections and resonances are found influenced by correlation and polarization effects. The non-relativistic molecular bremsstrahlung radiation cross-section for soft photons, binary encounter Bethe model-based ionization cross-sections and a few molecular properties of the target radical are also reported. The present calculations are found to be in agreement with the available results. This theoretical study provides a pathway to understand collision dynamics and generates data required in various fields of applied physics.

The amines are major source of environment pollutants emitted in atmosphere from variousanthropogenic sources. The non-thermal plasma (NTP)-based technology has proved successful in controlling the emitted amines reaching the atmosphere. The efficient NTP reactors rely on accurate electron–molecule collision data. The electron impact cross-sections are thus obtained for a few amines from ionisation threshold to 5000 eV using the single centre expansion (SCE) formalism. Themolecular wave function of each target is obtained from themulticentre expansion of the Gaussian-type orbitals within a single determinant Hartree–Fock self-consistent field scheme. The expansion of wave function, density and potential is carried out at the centre of mass of the molecules. The interaction potential included to model the electron interaction in the target comprises static, correlation polarisation and exchange types of potentials. The elastic cross-sections are obtained after solving the coupled scattering equations using Volterra integral form. The inelastic effects contributing to electron–molecule scatteringare approximated by the ionisation cross-sections. The total cross-sections obtained after summing the elastic and ionisation cross-sections are in good agreement with the available data. We have also tried to explain the effect of polarisation potential on scattering cross-sections. A semiempirical formula based on the spatial extent of the molecule is proposed to estimate the cross-sections for the homologous series of amine molecules.